If
is a
biased estimator for
, what is the amount of bias for this estimator if
and
?
a.The bias cannot be determined.
b.The bias is equal to 0.
c.The bias is equal to 1.
d.The bias is equal to -1.
Q. 2
Suppose a manufacturer, Company B, produces lawnmowers and a researcher is interested in the proportion of all lawnmowers purchased that are made by this manufacturer. A random sample of 150 individuals who purchased lawnmowers was taken and it was found that 42 of them purchased lawnmowers produced by Company B. Which of the following is an unbiased estimate of the population proportion of all lawnmowers purchased that are produced by Company B?
a.0.72
b.The population proportion is not known so an unbiased estimate cannot be determined.
c.0.28
d.42
Q. 3 Which of the following must be true for a point estimator,
, to be an unbiased estimator
?
a.
b.The variance of the sampling distribution of
equals
.
c.
d.
Q. 4
Which of the following statements is correct?
a.The population mean is a point estimate for the sample mean.
b.The sample mean is a point estimate for the population standard deviation.
c.The sample mean is a point estimate for the population mean.
d.The sample variance is a parameter.
Q. 5
Suppose a manufacturer produces computers in batches of 100. A researcher is interested in the proportion of all computers produced that are faulty so he randomly samples one batch and finds 9 faulty cameras. Which of the following would be a reasonable estimate of the population proportion of cameras that are not faulty?
a.9
b.0.91
c.0.09
d.91
Q. 6 Suppose the amount of propane used per customer in a month is normally distributed with
. Find a 95 confidence interval for
if a randomly chosen sample of 30 customers has a mean propane usage of 110 gallons a month.
a.(78.6, 141.4)
b.(103.2, 116.8)
c.(104.3, 115.7)
d.(105.2, 114.8)
Q. 7 Which of the following is
not a correct statement with regards to estimating a mean
using a known
?
a.The sampling distribution of
is normally distributed only if the sampled population is normally distributed.
b.A necessary assumption for estimating a mean
using a known
is that the sampling distribution of
is normally distributed.
c.If the sampling distribution for sample means
has a mean equal to
and a standard error equal to
and the randomly sampled population is normally distributed, then the sampling distribution of
has a normal distribution.
d.If the sampling distribution for sample means
has a mean equal to
and a standard error equal to
and the randomly sampled population is not normally distributed, then the sampling distribution of
is approximately normally distributed only for sufficiently large sample sizes.
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